The algorithm builds the histogram of the values of the indegree of all = nodes, which will be delivered in the two output files.

=20The network to analyze must be directed, otherwise there are no special = constraints.

=20Basic analysis tool, not particular for special disciplines or problems.=

=20The algorithm requires two inputs, the file where the edges of the netwo=
rk are listed and the number of points one wishes to have in the binned dis=
tribution described below. A first read-in of the inputfile will set the va=
lues of the number of nodes and edges of the network. In the second read-in=
the indegrees of all nodes will be calculated. Then the distribution is ca=
lculated.

The program generates two output files, corresponding to two =
different ways of partitioning the interval spanned by the values of indegr=
ee. In the first output, the occurrence of any indegree value between the m=
inimum and the maximum is estimated and divided by the number of nodes of t=
he network, so to obtain the probability: the output displays all indegree =
values in the interval with their probabilities.

The second output give=
s the *binned* distribution, i.e. the interval spanned by the values=
of indegree is divided into bins whose size grows while going to higher va=
lues of the variable. The size of each bin is obtained by multiplying by a =
fixed number the size of the previous bin. The program calculates the fract=
ion of nodes whose indegree falls within each bin. Because of the different=
sizes of the bins, these fractions must be divided by the respective bin s=
ize, to have meaningful averages.

This technique is particularly suitab=
le to study skewed distributions: the fact that the size of the bins grows =
large for large indegree values compensates for the fact that not many node=
s have high indegree values, so it suppresses the fluctuations that one wou=
ld observe by using bins of equal size. On a double logarithmic scale, whic=
h is very useful to determine the possible power law behavior of the distri=
bution, the points of the latter will appear equally spaced on the x-axis.<=
br> The program runs in a time O(m), m being the number of edges of the net=
work.

- =20
- Source Code =20

The algorithm was implemented and documented by S. Fortunato, integrated= by S. Fortunato and W. Huang.

=20Bollobas, B. (2002) Modern Graph Theory. Springer Verlag, New York.

= =20Albert, R., and Barabasi, A.-L. (2002) Statistical mechanics of complex networks. Review of Modern Phys= ics 74:47-97.

=20Newman, M.E.J. (2003) Th= e structure and function of complex networks. SIAM Review 45:167-256.=20

Pastor-Satorras, R., Vespignani, A.(2002) Evolution and Structure of the= Internet. Cambridge University Press.

=20Boccaletti, S., Latora, V., Moreno, Y.,Chavez, M., Hwang, D.-U.(2006) Complex networks: Structure and dynamics. Physics= Reports 424: 175-308.

=20
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